Managers shouldn't need that degree of transparency - expense policies are common, employees are not babies and should know the rules, and ultimately if an expense isn't justified the company isn't going to pay it anyway/deduct from wage (depending on whether it's personal card claim or corporate card based expenses)
I don't really buy #2, monthly expenses is common and hardly making them 'guilty until innocent'. If you have to sell your company to a potential hire as "having good expense claim policies" then you've got issues.
For #3, I would assume most finance teams would have existing systems in place to do the expense tracking itself (Expensify, some god-awful Oracle thing, etc) and so again, that's hardly a "win" and possibly a duplication. Foursquare characterization based on a checkin doesn't sound great compared to the heuristics that established software like Expensify already have in place.
Look, I wish you the best of luck with the launch but as someone who has been many years of filing and agreeing expense reports I just don't get where the sweetspot of need is this app fills.